The Ultimate Planar Convex Hull Algorithm ?

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Kirkpatrick, David G.; Seidel, Raimund

Abstract

We present a new planar convex hull algorithm with worst case time complexity $O(n \log H)$ where $n$ is the size of the input set and $H$ is the size of the output set, i.e. the number of vertices found to be on the hull. We also show that this algorithm is asymptotically worst case optimal on a rather realistic model of computation even if the complexity of the problem is measured in terms of input as well as output size. The algorithm relies on a variation of the divide-and-conquer paradigm which we call the "marriage-before-conquest" principle and which appears to be interesting in its own right.